A circuit is shown at the right containing a battery, four resistors, and a switch. The battery yields a potential difference of V₀ and the resistors have the following values: R_A =R_D = R and R_B = R_C = 3R.

(a) When the switch is open, find the current flowing through the battery. Express your answer in terms of the symbols V₀ and R. Show your reasoning.

(b) When the switch is closed, the current flowing through the battery is I₀. Is there any current flowing through the switch? If so, in which direction and how much? You may express your answer as a fraction of I₀ or in terms of V₀ and R.